Problem: $f(t) = -3t^{2}-7$ $g(t) = -2t^{3}+6t^{2}-t-6-2(f(t))$ $ f(g(6)) = {?} $
Solution: First, let's solve for the value of the inner function, $g(6)$ . Then we'll know what to plug into the outer function. $g(6) = -2(6^{3})+6(6^{2})-6-6-2(f(6))$ To solve for the value of $g$ , we need to solve for the value of $f(6)$ $f(6) = -3(6^{2})-7$ $f(6) = -115$ That means $g(6) = -2(6^{3})+6(6^{2})-6-6+(-2)(-115)$ $g(6) = 2$ Now we know that $g(6) = 2$ . Let's solve for $f(g(6))$ , which is $f(2)$ $f(2) = -3(2^{2})-7$ $f(2) = -19$